The Replacement Rule for Nonlinear Shallow Water Waves

Autor:	Zong, Zhi, Ludu, Andrei
Rok vydání:	2019
Předmět:	Nonlinear Sciences - Pattern Formation and Solitons Physics - Fluid Dynamics 35Q51 35Q53 35Q35 35Q30 35B36
Druh dokumentu:	Working Paper
Popis:	When a $(1+1)$-dimensional nonlinear PDE in real function $\eta(x,t)$ admits localized traveling solutions we can consider $L$ to be the average width of the envelope, $A$ the average value of the amplitude of the envelope, and $V$ the group velocity of such a solution. The replacement rule (RR or nonlinear dispersion relation) procedure is able to provide a simple qualitative relation between these three parameters, without actually solve the equation. Examples are provided from KdV, C-H and BBM equations, but the procedure appears to be almost universally valid for such $(1+1)$-dimensional nonlinear PDE and their localized traveling solutions \cite{3}. Comment: 12 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.11650 Zobrazit plný text záznamu View this record from Arxiv